Local well-posedness of compressible Radiation Hydrodynamic equations with density-dependent viscosities and vacuum
• Hao Li,
• Yachun Li
Hao Li
Shanghai Jiao Tong University
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Yachun Li
Shanghai Jiao Tong University
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## Abstract

In this paper, we consider the Cauchy problem for three-dimensional isentropic compressible radiation hydrodynamic equations with density-dependent viscosity coefficients. When the viscosity coefficients are given as power of density ($\rho^\delta$ with $\delta>1$), we establish the local-in-time existence of classical solutions containing a vacuum for large initial data. Here, we point out that the initial layer compatibility conditions are not necessary.

#### Peer review status:UNDER REVIEW

18 May 2020Submitted to Mathematical Methods in the Applied Sciences
23 May 2020Assigned to Editor
23 May 2020Submission Checks Completed
23 May 2020Reviewer(s) Assigned